Describe the location of firms and equilibrium , Basic Statistics

Take the Hotelling's location model (the linear city) discussed in class for the case in which all firms are required to charge the same fixed price. Further assume that firms choose their location sequentially (i.e. firm 1 moves first, followed by firm 2 etc.).

For simplicity make the following two assumptions:

1. Firm n knows the location of all n-1 firms that have already choose their location.

2. Firms can fully anticipate the number of firms that will (eventually) participate in the market.

(a) Describe the initial location of two firms and explain why these locations constitute an equilibrium location.

[Note: an 'equilibrium location' is the situation in which no firm wishes to relocate given the choice of all other firms.]

(b) Describe the initial location of three firms and explain why these locations constitute an equilibrium location.

(c) In the case of three firms, what happens to the intensity of direct-to-consumer spending and detailing for the first firm to enter the market as a function of entry? (i.e. how does firm 1 alters their DTCA and detailing expenditure when firm 2 enter and then when firm 3 enters the market?)